One key ingredient of guaranteeing fast convergence for RK and RCD is to construct an appropriate probability criterion used to select \(_i^T\)  and \(_j\)  from \(A\) , respectively. The promising adaptive index selection was introduced in Bai and Wu's series of work [1]}, [2]}, [3]}, where the authors applied it to RK and RCD, and presented the greedy RK (GRK [1]}, RGRK [2]}) and RCD (GRCD [3]}) methods.
The relaxed version of GRCD (RGRCD) is given by [7]}. The relaxed greedy row and column selection strategies were enlarged to more general cases by Gower et al. [8]}.
